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What is the vertex of the quadratic function f(x) = (x – 6)(x + 2)?

1 Answer

4 votes

Answer:

The vertex is (2,-16)

Explanation:

The given function is
f(x)=(x-6)(x+2)

We expand to obtain;


f(x)=x^2+2x-6x-12


f(x)=x^2-4x-12

We complete the squares to obtain;


f(x)=x^2-4x+(-2)^2-12-(-2)^2


f(x)=x^2-4x+(-2)^2-12-4


f(x)=(x-2)^2-16

The vertex form is
f(x)=(x-2)^2-16

Comparing this to


f(x)=a(x-k)^2+k

The vertex is (h,k)= (2,-16)

User George Anderson
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